Consider the constant function f(x) = 2. To find the limit of f(x) as `x to 3`.

Options

A. 0
B. 1
C. -1
D. 2

Answer

To find the limit of the constant function \( f(x) = 2 \) as \( x \) approaches 3, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Function**: We have the constant function \( f(x) = 2 \). This means that for any value of \( x \), the output of the function is always 2.

2. **Understand the Concept of Limits**: The limit of a function as \( x \) approaches a certain value (in this case, 3) is the value that the function approaches as \( x \) gets closer to that value.

3. **Evaluate the Limit**: Since \( f(x) \) is a constant function, it does not change regardless of the value of \( x \). Therefore, as \( x \) approaches 3, the value of \( f(x) \) remains 2.

4. **Write the Limit Statement**: We can express this mathematically as:
\[ \lim_{x \to 3} f(x) = \lim_{x \to 3} 2 \]

5. **Conclude the Limit**: Since the function is constant, the limit is simply the value of the constant:
\[ \lim_{x \to 3} f(x) = 2 \]

### Final Answer:
The limit of \( f(x) \) as \( x \) approaches 3 is \( 2 \).

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